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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.complex;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.io.Serializable;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.Precision;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.ZeroException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * This class implements &lt;a href="http://mathworld.wolfram.com/Quaternion.html"&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * quaternions&lt;/a&gt; (Hamilton's hypercomplex numbers).<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;br/&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * Instance of this class are guaranteed to be immutable.<a name="line.32"></a>
<FONT color="green">033</FONT>     *<a name="line.33"></a>
<FONT color="green">034</FONT>     * @since 3.1<a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Id: Quaternion.java 1421249 2012-12-13 12:32:03Z erans $<a name="line.35"></a>
<FONT color="green">036</FONT>     */<a name="line.36"></a>
<FONT color="green">037</FONT>    public final class Quaternion implements Serializable {<a name="line.37"></a>
<FONT color="green">038</FONT>        /** Identity quaternion. */<a name="line.38"></a>
<FONT color="green">039</FONT>        public static final Quaternion IDENTITY = new Quaternion(1, 0, 0, 0);<a name="line.39"></a>
<FONT color="green">040</FONT>        /** Zero quaternion. */<a name="line.40"></a>
<FONT color="green">041</FONT>        public static final Quaternion ZERO = new Quaternion(0, 0, 0, 0);<a name="line.41"></a>
<FONT color="green">042</FONT>        /** i */<a name="line.42"></a>
<FONT color="green">043</FONT>        public static final Quaternion I = new Quaternion(0, 1, 0, 0);<a name="line.43"></a>
<FONT color="green">044</FONT>        /** j */<a name="line.44"></a>
<FONT color="green">045</FONT>        public static final Quaternion J = new Quaternion(0, 0, 1, 0);<a name="line.45"></a>
<FONT color="green">046</FONT>        /** k */<a name="line.46"></a>
<FONT color="green">047</FONT>        public static final Quaternion K = new Quaternion(0, 0, 0, 1);<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>        /** Serializable version identifier. */<a name="line.49"></a>
<FONT color="green">050</FONT>        private static final long serialVersionUID = 20092012L;<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>        /** First component (scalar part). */<a name="line.52"></a>
<FONT color="green">053</FONT>        private final double q0;<a name="line.53"></a>
<FONT color="green">054</FONT>        /** Second component (first vector part). */<a name="line.54"></a>
<FONT color="green">055</FONT>        private final double q1;<a name="line.55"></a>
<FONT color="green">056</FONT>        /** Third component (second vector part). */<a name="line.56"></a>
<FONT color="green">057</FONT>        private final double q2;<a name="line.57"></a>
<FONT color="green">058</FONT>        /** Fourth component (third vector part). */<a name="line.58"></a>
<FONT color="green">059</FONT>        private final double q3;<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>        /**<a name="line.61"></a>
<FONT color="green">062</FONT>         * Builds a quaternion from its components.<a name="line.62"></a>
<FONT color="green">063</FONT>         *<a name="line.63"></a>
<FONT color="green">064</FONT>         * @param a Scalar component.<a name="line.64"></a>
<FONT color="green">065</FONT>         * @param b First vector component.<a name="line.65"></a>
<FONT color="green">066</FONT>         * @param c Second vector component.<a name="line.66"></a>
<FONT color="green">067</FONT>         * @param d Third vector component.<a name="line.67"></a>
<FONT color="green">068</FONT>         */<a name="line.68"></a>
<FONT color="green">069</FONT>        public Quaternion(final double a,<a name="line.69"></a>
<FONT color="green">070</FONT>                          final double b,<a name="line.70"></a>
<FONT color="green">071</FONT>                          final double c,<a name="line.71"></a>
<FONT color="green">072</FONT>                          final double d) {<a name="line.72"></a>
<FONT color="green">073</FONT>            this.q0 = a;<a name="line.73"></a>
<FONT color="green">074</FONT>            this.q1 = b;<a name="line.74"></a>
<FONT color="green">075</FONT>            this.q2 = c;<a name="line.75"></a>
<FONT color="green">076</FONT>            this.q3 = d;<a name="line.76"></a>
<FONT color="green">077</FONT>        }<a name="line.77"></a>
<FONT color="green">078</FONT>    <a name="line.78"></a>
<FONT color="green">079</FONT>        /**<a name="line.79"></a>
<FONT color="green">080</FONT>         * Builds a quaternion from scalar and vector parts.<a name="line.80"></a>
<FONT color="green">081</FONT>         *<a name="line.81"></a>
<FONT color="green">082</FONT>         * @param scalar Scalar part of the quaternion.<a name="line.82"></a>
<FONT color="green">083</FONT>         * @param v Components of the vector part of the quaternion.<a name="line.83"></a>
<FONT color="green">084</FONT>         *<a name="line.84"></a>
<FONT color="green">085</FONT>         * @throws DimensionMismatchException if the array length is not 3.<a name="line.85"></a>
<FONT color="green">086</FONT>         */<a name="line.86"></a>
<FONT color="green">087</FONT>        public Quaternion(final double scalar,<a name="line.87"></a>
<FONT color="green">088</FONT>                          final double[] v)<a name="line.88"></a>
<FONT color="green">089</FONT>            throws DimensionMismatchException {<a name="line.89"></a>
<FONT color="green">090</FONT>            if (v.length != 3) {<a name="line.90"></a>
<FONT color="green">091</FONT>                throw new DimensionMismatchException(v.length, 3);<a name="line.91"></a>
<FONT color="green">092</FONT>            }<a name="line.92"></a>
<FONT color="green">093</FONT>            this.q0 = scalar;<a name="line.93"></a>
<FONT color="green">094</FONT>            this.q1 = v[0];<a name="line.94"></a>
<FONT color="green">095</FONT>            this.q2 = v[1];<a name="line.95"></a>
<FONT color="green">096</FONT>            this.q3 = v[2];<a name="line.96"></a>
<FONT color="green">097</FONT>        }<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /**<a name="line.99"></a>
<FONT color="green">100</FONT>         * Builds a pure quaternion from a vector (assuming that the scalar<a name="line.100"></a>
<FONT color="green">101</FONT>         * part is zero).<a name="line.101"></a>
<FONT color="green">102</FONT>         *<a name="line.102"></a>
<FONT color="green">103</FONT>         * @param v Components of the vector part of the pure quaternion.<a name="line.103"></a>
<FONT color="green">104</FONT>         */<a name="line.104"></a>
<FONT color="green">105</FONT>        public Quaternion(final double[] v) {<a name="line.105"></a>
<FONT color="green">106</FONT>            this(0, v);<a name="line.106"></a>
<FONT color="green">107</FONT>        }<a name="line.107"></a>
<FONT color="green">108</FONT>    <a name="line.108"></a>
<FONT color="green">109</FONT>        /**<a name="line.109"></a>
<FONT color="green">110</FONT>         * Returns the conjugate quaternion of the instance.<a name="line.110"></a>
<FONT color="green">111</FONT>         *<a name="line.111"></a>
<FONT color="green">112</FONT>         * @return the conjugate quaternion<a name="line.112"></a>
<FONT color="green">113</FONT>         */<a name="line.113"></a>
<FONT color="green">114</FONT>        public Quaternion getConjugate() {<a name="line.114"></a>
<FONT color="green">115</FONT>            return new Quaternion(q0, -q1, -q2, -q3);<a name="line.115"></a>
<FONT color="green">116</FONT>        }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>        /**<a name="line.118"></a>
<FONT color="green">119</FONT>         * Returns the Hamilton product of two quaternions.<a name="line.119"></a>
<FONT color="green">120</FONT>         *<a name="line.120"></a>
<FONT color="green">121</FONT>         * @param q1 First quaternion.<a name="line.121"></a>
<FONT color="green">122</FONT>         * @param q2 Second quaternion.<a name="line.122"></a>
<FONT color="green">123</FONT>         * @return the product {@code q1} and {@code q2}, in that order.<a name="line.123"></a>
<FONT color="green">124</FONT>         */<a name="line.124"></a>
<FONT color="green">125</FONT>        public static Quaternion multiply(final Quaternion q1, final Quaternion q2) {<a name="line.125"></a>
<FONT color="green">126</FONT>            // Components of the first quaternion.<a name="line.126"></a>
<FONT color="green">127</FONT>            final double q1a = q1.getQ0();<a name="line.127"></a>
<FONT color="green">128</FONT>            final double q1b = q1.getQ1();<a name="line.128"></a>
<FONT color="green">129</FONT>            final double q1c = q1.getQ2();<a name="line.129"></a>
<FONT color="green">130</FONT>            final double q1d = q1.getQ3();<a name="line.130"></a>
<FONT color="green">131</FONT>    <a name="line.131"></a>
<FONT color="green">132</FONT>            // Components of the second quaternion.<a name="line.132"></a>
<FONT color="green">133</FONT>            final double q2a = q2.getQ0();<a name="line.133"></a>
<FONT color="green">134</FONT>            final double q2b = q2.getQ1();<a name="line.134"></a>
<FONT color="green">135</FONT>            final double q2c = q2.getQ2();<a name="line.135"></a>
<FONT color="green">136</FONT>            final double q2d = q2.getQ3();<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>            // Components of the product.<a name="line.138"></a>
<FONT color="green">139</FONT>            final double w = q1a * q2a - q1b * q2b - q1c * q2c - q1d * q2d;<a name="line.139"></a>
<FONT color="green">140</FONT>            final double x = q1a * q2b + q1b * q2a + q1c * q2d - q1d * q2c;<a name="line.140"></a>
<FONT color="green">141</FONT>            final double y = q1a * q2c - q1b * q2d + q1c * q2a + q1d * q2b;<a name="line.141"></a>
<FONT color="green">142</FONT>            final double z = q1a * q2d + q1b * q2c - q1c * q2b + q1d * q2a;<a name="line.142"></a>
<FONT color="green">143</FONT>    <a name="line.143"></a>
<FONT color="green">144</FONT>            return new Quaternion(w, x, y, z);<a name="line.144"></a>
<FONT color="green">145</FONT>        }<a name="line.145"></a>
<FONT color="green">146</FONT>    <a name="line.146"></a>
<FONT color="green">147</FONT>        /**<a name="line.147"></a>
<FONT color="green">148</FONT>         * Returns the Hamilton product of the instance by a quaternion.<a name="line.148"></a>
<FONT color="green">149</FONT>         *<a name="line.149"></a>
<FONT color="green">150</FONT>         * @param q Quaternion.<a name="line.150"></a>
<FONT color="green">151</FONT>         * @return the product of this instance with {@code q}, in that order.<a name="line.151"></a>
<FONT color="green">152</FONT>         */<a name="line.152"></a>
<FONT color="green">153</FONT>        public Quaternion multiply(final Quaternion q) {<a name="line.153"></a>
<FONT color="green">154</FONT>            return multiply(this, q);<a name="line.154"></a>
<FONT color="green">155</FONT>        }<a name="line.155"></a>
<FONT color="green">156</FONT>    <a name="line.156"></a>
<FONT color="green">157</FONT>        /**<a name="line.157"></a>
<FONT color="green">158</FONT>         * Computes the sum of two quaternions.<a name="line.158"></a>
<FONT color="green">159</FONT>         *<a name="line.159"></a>
<FONT color="green">160</FONT>         * @param q1 Quaternion.<a name="line.160"></a>
<FONT color="green">161</FONT>         * @param q2 Quaternion.<a name="line.161"></a>
<FONT color="green">162</FONT>         * @return the sum of {@code q1} and {@code q2}.<a name="line.162"></a>
<FONT color="green">163</FONT>         */<a name="line.163"></a>
<FONT color="green">164</FONT>        public static Quaternion add(final Quaternion q1,<a name="line.164"></a>
<FONT color="green">165</FONT>                                     final Quaternion q2) {<a name="line.165"></a>
<FONT color="green">166</FONT>            return new Quaternion(q1.getQ0() + q2.getQ0(),<a name="line.166"></a>
<FONT color="green">167</FONT>                                  q1.getQ1() + q2.getQ1(),<a name="line.167"></a>
<FONT color="green">168</FONT>                                  q1.getQ2() + q2.getQ2(),<a name="line.168"></a>
<FONT color="green">169</FONT>                                  q1.getQ3() + q2.getQ3());<a name="line.169"></a>
<FONT color="green">170</FONT>        }<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>        /**<a name="line.172"></a>
<FONT color="green">173</FONT>         * Computes the sum of the instance and another quaternion.<a name="line.173"></a>
<FONT color="green">174</FONT>         *<a name="line.174"></a>
<FONT color="green">175</FONT>         * @param q Quaternion.<a name="line.175"></a>
<FONT color="green">176</FONT>         * @return the sum of this instance and {@code q}<a name="line.176"></a>
<FONT color="green">177</FONT>         */<a name="line.177"></a>
<FONT color="green">178</FONT>        public Quaternion add(final Quaternion q) {<a name="line.178"></a>
<FONT color="green">179</FONT>            return add(this, q);<a name="line.179"></a>
<FONT color="green">180</FONT>        }<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>        /**<a name="line.182"></a>
<FONT color="green">183</FONT>         * Subtracts two quaternions.<a name="line.183"></a>
<FONT color="green">184</FONT>         *<a name="line.184"></a>
<FONT color="green">185</FONT>         * @param q1 First Quaternion.<a name="line.185"></a>
<FONT color="green">186</FONT>         * @param q2 Second quaternion.<a name="line.186"></a>
<FONT color="green">187</FONT>         * @return the difference between {@code q1} and {@code q2}.<a name="line.187"></a>
<FONT color="green">188</FONT>         */<a name="line.188"></a>
<FONT color="green">189</FONT>        public static Quaternion subtract(final Quaternion q1,<a name="line.189"></a>
<FONT color="green">190</FONT>                                          final Quaternion q2) {<a name="line.190"></a>
<FONT color="green">191</FONT>            return new Quaternion(q1.getQ0() - q2.getQ0(),<a name="line.191"></a>
<FONT color="green">192</FONT>                                  q1.getQ1() - q2.getQ1(),<a name="line.192"></a>
<FONT color="green">193</FONT>                                  q1.getQ2() - q2.getQ2(),<a name="line.193"></a>
<FONT color="green">194</FONT>                                  q1.getQ3() - q2.getQ3());<a name="line.194"></a>
<FONT color="green">195</FONT>        }<a name="line.195"></a>
<FONT color="green">196</FONT>    <a name="line.196"></a>
<FONT color="green">197</FONT>        /**<a name="line.197"></a>
<FONT color="green">198</FONT>         * Subtracts a quaternion from the instance.<a name="line.198"></a>
<FONT color="green">199</FONT>         *<a name="line.199"></a>
<FONT color="green">200</FONT>         * @param q Quaternion.<a name="line.200"></a>
<FONT color="green">201</FONT>         * @return the difference between this instance and {@code q}.<a name="line.201"></a>
<FONT color="green">202</FONT>         */<a name="line.202"></a>
<FONT color="green">203</FONT>        public Quaternion subtract(final Quaternion q) {<a name="line.203"></a>
<FONT color="green">204</FONT>            return subtract(this, q);<a name="line.204"></a>
<FONT color="green">205</FONT>        }<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>        /**<a name="line.207"></a>
<FONT color="green">208</FONT>         * Computes the dot-product of two quaternions.<a name="line.208"></a>
<FONT color="green">209</FONT>         *<a name="line.209"></a>
<FONT color="green">210</FONT>         * @param q1 Quaternion.<a name="line.210"></a>
<FONT color="green">211</FONT>         * @param q2 Quaternion.<a name="line.211"></a>
<FONT color="green">212</FONT>         * @return the dot product of {@code q1} and {@code q2}.<a name="line.212"></a>
<FONT color="green">213</FONT>         */<a name="line.213"></a>
<FONT color="green">214</FONT>        public static double dotProduct(final Quaternion q1,<a name="line.214"></a>
<FONT color="green">215</FONT>                                        final Quaternion q2) {<a name="line.215"></a>
<FONT color="green">216</FONT>            return q1.getQ0() * q2.getQ0() +<a name="line.216"></a>
<FONT color="green">217</FONT>                q1.getQ1() * q2.getQ1() +<a name="line.217"></a>
<FONT color="green">218</FONT>                q1.getQ2() * q2.getQ2() +<a name="line.218"></a>
<FONT color="green">219</FONT>                q1.getQ3() * q2.getQ3();<a name="line.219"></a>
<FONT color="green">220</FONT>        }<a name="line.220"></a>
<FONT color="green">221</FONT>    <a name="line.221"></a>
<FONT color="green">222</FONT>        /**<a name="line.222"></a>
<FONT color="green">223</FONT>         * Computes the dot-product of the instance by a quaternion.<a name="line.223"></a>
<FONT color="green">224</FONT>         *<a name="line.224"></a>
<FONT color="green">225</FONT>         * @param q Quaternion.<a name="line.225"></a>
<FONT color="green">226</FONT>         * @return the dot product of this instance and {@code q}.<a name="line.226"></a>
<FONT color="green">227</FONT>         */<a name="line.227"></a>
<FONT color="green">228</FONT>        public double dotProduct(final Quaternion q) {<a name="line.228"></a>
<FONT color="green">229</FONT>            return dotProduct(this, q);<a name="line.229"></a>
<FONT color="green">230</FONT>        }<a name="line.230"></a>
<FONT color="green">231</FONT>    <a name="line.231"></a>
<FONT color="green">232</FONT>        /**<a name="line.232"></a>
<FONT color="green">233</FONT>         * Computes the norm of the quaternion.<a name="line.233"></a>
<FONT color="green">234</FONT>         *<a name="line.234"></a>
<FONT color="green">235</FONT>         * @return the norm.<a name="line.235"></a>
<FONT color="green">236</FONT>         */<a name="line.236"></a>
<FONT color="green">237</FONT>        public double getNorm() {<a name="line.237"></a>
<FONT color="green">238</FONT>            return FastMath.sqrt(q0 * q0 +<a name="line.238"></a>
<FONT color="green">239</FONT>                                 q1 * q1 +<a name="line.239"></a>
<FONT color="green">240</FONT>                                 q2 * q2 +<a name="line.240"></a>
<FONT color="green">241</FONT>                                 q3 * q3);<a name="line.241"></a>
<FONT color="green">242</FONT>        }<a name="line.242"></a>
<FONT color="green">243</FONT>    <a name="line.243"></a>
<FONT color="green">244</FONT>        /**<a name="line.244"></a>
<FONT color="green">245</FONT>         * Computes the normalized quaternion (the versor of the instance).<a name="line.245"></a>
<FONT color="green">246</FONT>         * The norm of the quaternion must not be zero.<a name="line.246"></a>
<FONT color="green">247</FONT>         *<a name="line.247"></a>
<FONT color="green">248</FONT>         * @return a normalized quaternion.<a name="line.248"></a>
<FONT color="green">249</FONT>         * @throws ZeroException if the norm of the quaternion is zero.<a name="line.249"></a>
<FONT color="green">250</FONT>         */<a name="line.250"></a>
<FONT color="green">251</FONT>        public Quaternion normalize() {<a name="line.251"></a>
<FONT color="green">252</FONT>            final double norm = getNorm();<a name="line.252"></a>
<FONT color="green">253</FONT>    <a name="line.253"></a>
<FONT color="green">254</FONT>            if (norm &lt; Precision.SAFE_MIN) {<a name="line.254"></a>
<FONT color="green">255</FONT>                throw new ZeroException(LocalizedFormats.NORM, norm);<a name="line.255"></a>
<FONT color="green">256</FONT>            }<a name="line.256"></a>
<FONT color="green">257</FONT>    <a name="line.257"></a>
<FONT color="green">258</FONT>            return new Quaternion(q0 / norm,<a name="line.258"></a>
<FONT color="green">259</FONT>                                  q1 / norm,<a name="line.259"></a>
<FONT color="green">260</FONT>                                  q2 / norm,<a name="line.260"></a>
<FONT color="green">261</FONT>                                  q3 / norm);<a name="line.261"></a>
<FONT color="green">262</FONT>        }<a name="line.262"></a>
<FONT color="green">263</FONT>    <a name="line.263"></a>
<FONT color="green">264</FONT>        /**<a name="line.264"></a>
<FONT color="green">265</FONT>         * {@inheritDoc}<a name="line.265"></a>
<FONT color="green">266</FONT>         */<a name="line.266"></a>
<FONT color="green">267</FONT>        @Override<a name="line.267"></a>
<FONT color="green">268</FONT>        public boolean equals(Object other) {<a name="line.268"></a>
<FONT color="green">269</FONT>            if (this == other) {<a name="line.269"></a>
<FONT color="green">270</FONT>                return true;<a name="line.270"></a>
<FONT color="green">271</FONT>            }<a name="line.271"></a>
<FONT color="green">272</FONT>            if (other instanceof Quaternion) {<a name="line.272"></a>
<FONT color="green">273</FONT>                final Quaternion q = (Quaternion) other;<a name="line.273"></a>
<FONT color="green">274</FONT>                return q0 == q.getQ0() &amp;&amp;<a name="line.274"></a>
<FONT color="green">275</FONT>                    q1 == q.getQ1() &amp;&amp;<a name="line.275"></a>
<FONT color="green">276</FONT>                    q2 == q.getQ2() &amp;&amp;<a name="line.276"></a>
<FONT color="green">277</FONT>                    q3 == q.getQ3();<a name="line.277"></a>
<FONT color="green">278</FONT>            }<a name="line.278"></a>
<FONT color="green">279</FONT>    <a name="line.279"></a>
<FONT color="green">280</FONT>            return false;<a name="line.280"></a>
<FONT color="green">281</FONT>        }<a name="line.281"></a>
<FONT color="green">282</FONT>    <a name="line.282"></a>
<FONT color="green">283</FONT>        /**<a name="line.283"></a>
<FONT color="green">284</FONT>         * {@inheritDoc}<a name="line.284"></a>
<FONT color="green">285</FONT>         */<a name="line.285"></a>
<FONT color="green">286</FONT>        @Override<a name="line.286"></a>
<FONT color="green">287</FONT>        public int hashCode() {<a name="line.287"></a>
<FONT color="green">288</FONT>            // "Effective Java" (second edition, p. 47).<a name="line.288"></a>
<FONT color="green">289</FONT>            int result = 17;<a name="line.289"></a>
<FONT color="green">290</FONT>            for (double comp : new double[] { q0, q1, q2, q3 }) {<a name="line.290"></a>
<FONT color="green">291</FONT>                final int c = MathUtils.hash(comp);<a name="line.291"></a>
<FONT color="green">292</FONT>                result = 31 * result + c;<a name="line.292"></a>
<FONT color="green">293</FONT>            }<a name="line.293"></a>
<FONT color="green">294</FONT>            return result;<a name="line.294"></a>
<FONT color="green">295</FONT>        }<a name="line.295"></a>
<FONT color="green">296</FONT>    <a name="line.296"></a>
<FONT color="green">297</FONT>        /**<a name="line.297"></a>
<FONT color="green">298</FONT>         * Checks whether this instance is equal to another quaternion<a name="line.298"></a>
<FONT color="green">299</FONT>         * within a given tolerance.<a name="line.299"></a>
<FONT color="green">300</FONT>         *<a name="line.300"></a>
<FONT color="green">301</FONT>         * @param q Quaternion with which to compare the current quaternion.<a name="line.301"></a>
<FONT color="green">302</FONT>         * @param eps Tolerance.<a name="line.302"></a>
<FONT color="green">303</FONT>         * @return {@code true} if the each of the components are equal<a name="line.303"></a>
<FONT color="green">304</FONT>         * within the allowed absolute error.<a name="line.304"></a>
<FONT color="green">305</FONT>         */<a name="line.305"></a>
<FONT color="green">306</FONT>        public boolean equals(final Quaternion q,<a name="line.306"></a>
<FONT color="green">307</FONT>                              final double eps) {<a name="line.307"></a>
<FONT color="green">308</FONT>            return Precision.equals(q0, q.getQ0(), eps) &amp;&amp;<a name="line.308"></a>
<FONT color="green">309</FONT>                Precision.equals(q1, q.getQ1(), eps) &amp;&amp;<a name="line.309"></a>
<FONT color="green">310</FONT>                Precision.equals(q2, q.getQ2(), eps) &amp;&amp;<a name="line.310"></a>
<FONT color="green">311</FONT>                Precision.equals(q3, q.getQ3(), eps);<a name="line.311"></a>
<FONT color="green">312</FONT>        }<a name="line.312"></a>
<FONT color="green">313</FONT>    <a name="line.313"></a>
<FONT color="green">314</FONT>        /**<a name="line.314"></a>
<FONT color="green">315</FONT>         * Checks whether the instance is a unit quaternion within a given<a name="line.315"></a>
<FONT color="green">316</FONT>         * tolerance.<a name="line.316"></a>
<FONT color="green">317</FONT>         *<a name="line.317"></a>
<FONT color="green">318</FONT>         * @param eps Tolerance (absolute error).<a name="line.318"></a>
<FONT color="green">319</FONT>         * @return {@code true} if the norm is 1 within the given tolerance,<a name="line.319"></a>
<FONT color="green">320</FONT>         * {@code false} otherwise<a name="line.320"></a>
<FONT color="green">321</FONT>         */<a name="line.321"></a>
<FONT color="green">322</FONT>        public boolean isUnitQuaternion(double eps) {<a name="line.322"></a>
<FONT color="green">323</FONT>            return Precision.equals(getNorm(), 1d, eps);<a name="line.323"></a>
<FONT color="green">324</FONT>        }<a name="line.324"></a>
<FONT color="green">325</FONT>    <a name="line.325"></a>
<FONT color="green">326</FONT>        /**<a name="line.326"></a>
<FONT color="green">327</FONT>         * Checks whether the instance is a pure quaternion within a given<a name="line.327"></a>
<FONT color="green">328</FONT>         * tolerance.<a name="line.328"></a>
<FONT color="green">329</FONT>         *<a name="line.329"></a>
<FONT color="green">330</FONT>         * @param eps Tolerance (absolute error).<a name="line.330"></a>
<FONT color="green">331</FONT>         * @return {@code true} if the scalar part of the quaternion is zero.<a name="line.331"></a>
<FONT color="green">332</FONT>         */<a name="line.332"></a>
<FONT color="green">333</FONT>        public boolean isPureQuaternion(double eps) {<a name="line.333"></a>
<FONT color="green">334</FONT>            return FastMath.abs(getQ0()) &lt;= eps;<a name="line.334"></a>
<FONT color="green">335</FONT>        }<a name="line.335"></a>
<FONT color="green">336</FONT>    <a name="line.336"></a>
<FONT color="green">337</FONT>        /**<a name="line.337"></a>
<FONT color="green">338</FONT>         * Returns the polar form of the quaternion.<a name="line.338"></a>
<FONT color="green">339</FONT>         *<a name="line.339"></a>
<FONT color="green">340</FONT>         * @return the unit quaternion with positive scalar part.<a name="line.340"></a>
<FONT color="green">341</FONT>         */<a name="line.341"></a>
<FONT color="green">342</FONT>        public Quaternion getPositivePolarForm() {<a name="line.342"></a>
<FONT color="green">343</FONT>            if (getQ0() &lt; 0) {<a name="line.343"></a>
<FONT color="green">344</FONT>                final Quaternion unitQ = normalize();<a name="line.344"></a>
<FONT color="green">345</FONT>                // The quaternion of rotation (normalized quaternion) q and -q<a name="line.345"></a>
<FONT color="green">346</FONT>                // are equivalent (i.e. represent the same rotation).<a name="line.346"></a>
<FONT color="green">347</FONT>                return new Quaternion(-unitQ.getQ0(),<a name="line.347"></a>
<FONT color="green">348</FONT>                                      -unitQ.getQ1(),<a name="line.348"></a>
<FONT color="green">349</FONT>                                      -unitQ.getQ2(),<a name="line.349"></a>
<FONT color="green">350</FONT>                                      -unitQ.getQ3());<a name="line.350"></a>
<FONT color="green">351</FONT>            } else {<a name="line.351"></a>
<FONT color="green">352</FONT>                return this.normalize();<a name="line.352"></a>
<FONT color="green">353</FONT>            }<a name="line.353"></a>
<FONT color="green">354</FONT>        }<a name="line.354"></a>
<FONT color="green">355</FONT>    <a name="line.355"></a>
<FONT color="green">356</FONT>        /**<a name="line.356"></a>
<FONT color="green">357</FONT>         * Returns the inverse of this instance.<a name="line.357"></a>
<FONT color="green">358</FONT>         * The norm of the quaternion must not be zero.<a name="line.358"></a>
<FONT color="green">359</FONT>         *<a name="line.359"></a>
<FONT color="green">360</FONT>         * @return the inverse.<a name="line.360"></a>
<FONT color="green">361</FONT>         * @throws ZeroException if the norm (squared) of the quaternion is zero.<a name="line.361"></a>
<FONT color="green">362</FONT>         */<a name="line.362"></a>
<FONT color="green">363</FONT>        public Quaternion getInverse() {<a name="line.363"></a>
<FONT color="green">364</FONT>            final double squareNorm = q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3;<a name="line.364"></a>
<FONT color="green">365</FONT>            if (squareNorm &lt; Precision.SAFE_MIN) {<a name="line.365"></a>
<FONT color="green">366</FONT>                throw new ZeroException(LocalizedFormats.NORM, squareNorm);<a name="line.366"></a>
<FONT color="green">367</FONT>            }<a name="line.367"></a>
<FONT color="green">368</FONT>    <a name="line.368"></a>
<FONT color="green">369</FONT>            return new Quaternion(q0 / squareNorm,<a name="line.369"></a>
<FONT color="green">370</FONT>                                  -q1 / squareNorm,<a name="line.370"></a>
<FONT color="green">371</FONT>                                  -q2 / squareNorm,<a name="line.371"></a>
<FONT color="green">372</FONT>                                  -q3 / squareNorm);<a name="line.372"></a>
<FONT color="green">373</FONT>        }<a name="line.373"></a>
<FONT color="green">374</FONT>    <a name="line.374"></a>
<FONT color="green">375</FONT>        /**<a name="line.375"></a>
<FONT color="green">376</FONT>         * Gets the first component of the quaternion (scalar part).<a name="line.376"></a>
<FONT color="green">377</FONT>         *<a name="line.377"></a>
<FONT color="green">378</FONT>         * @return the scalar part.<a name="line.378"></a>
<FONT color="green">379</FONT>         */<a name="line.379"></a>
<FONT color="green">380</FONT>        public double getQ0() {<a name="line.380"></a>
<FONT color="green">381</FONT>            return q0;<a name="line.381"></a>
<FONT color="green">382</FONT>        }<a name="line.382"></a>
<FONT color="green">383</FONT>    <a name="line.383"></a>
<FONT color="green">384</FONT>        /**<a name="line.384"></a>
<FONT color="green">385</FONT>         * Gets the second component of the quaternion (first component<a name="line.385"></a>
<FONT color="green">386</FONT>         * of the vector part).<a name="line.386"></a>
<FONT color="green">387</FONT>         *<a name="line.387"></a>
<FONT color="green">388</FONT>         * @return the first component of the vector part.<a name="line.388"></a>
<FONT color="green">389</FONT>         */<a name="line.389"></a>
<FONT color="green">390</FONT>        public double getQ1() {<a name="line.390"></a>
<FONT color="green">391</FONT>            return q1;<a name="line.391"></a>
<FONT color="green">392</FONT>        }<a name="line.392"></a>
<FONT color="green">393</FONT>    <a name="line.393"></a>
<FONT color="green">394</FONT>        /**<a name="line.394"></a>
<FONT color="green">395</FONT>         * Gets the third component of the quaternion (second component<a name="line.395"></a>
<FONT color="green">396</FONT>         * of the vector part).<a name="line.396"></a>
<FONT color="green">397</FONT>         *<a name="line.397"></a>
<FONT color="green">398</FONT>         * @return the second component of the vector part.<a name="line.398"></a>
<FONT color="green">399</FONT>         */<a name="line.399"></a>
<FONT color="green">400</FONT>        public double getQ2() {<a name="line.400"></a>
<FONT color="green">401</FONT>            return q2;<a name="line.401"></a>
<FONT color="green">402</FONT>        }<a name="line.402"></a>
<FONT color="green">403</FONT>    <a name="line.403"></a>
<FONT color="green">404</FONT>        /**<a name="line.404"></a>
<FONT color="green">405</FONT>         * Gets the fourth component of the quaternion (third component<a name="line.405"></a>
<FONT color="green">406</FONT>         * of the vector part).<a name="line.406"></a>
<FONT color="green">407</FONT>         *<a name="line.407"></a>
<FONT color="green">408</FONT>         * @return the third component of the vector part.<a name="line.408"></a>
<FONT color="green">409</FONT>         */<a name="line.409"></a>
<FONT color="green">410</FONT>        public double getQ3() {<a name="line.410"></a>
<FONT color="green">411</FONT>            return q3;<a name="line.411"></a>
<FONT color="green">412</FONT>        }<a name="line.412"></a>
<FONT color="green">413</FONT>    <a name="line.413"></a>
<FONT color="green">414</FONT>        /**<a name="line.414"></a>
<FONT color="green">415</FONT>         * Gets the scalar part of the quaternion.<a name="line.415"></a>
<FONT color="green">416</FONT>         *<a name="line.416"></a>
<FONT color="green">417</FONT>         * @return the scalar part.<a name="line.417"></a>
<FONT color="green">418</FONT>         * @see #getQ0()<a name="line.418"></a>
<FONT color="green">419</FONT>         */<a name="line.419"></a>
<FONT color="green">420</FONT>        public double getScalarPart() {<a name="line.420"></a>
<FONT color="green">421</FONT>            return getQ0();<a name="line.421"></a>
<FONT color="green">422</FONT>        }<a name="line.422"></a>
<FONT color="green">423</FONT>    <a name="line.423"></a>
<FONT color="green">424</FONT>        /**<a name="line.424"></a>
<FONT color="green">425</FONT>         * Gets the three components of the vector part of the quaternion.<a name="line.425"></a>
<FONT color="green">426</FONT>         *<a name="line.426"></a>
<FONT color="green">427</FONT>         * @return the vector part.<a name="line.427"></a>
<FONT color="green">428</FONT>         * @see #getQ1()<a name="line.428"></a>
<FONT color="green">429</FONT>         * @see #getQ2()<a name="line.429"></a>
<FONT color="green">430</FONT>         * @see #getQ3()<a name="line.430"></a>
<FONT color="green">431</FONT>         */<a name="line.431"></a>
<FONT color="green">432</FONT>        public double[] getVectorPart() {<a name="line.432"></a>
<FONT color="green">433</FONT>            return new double[] { getQ1(), getQ2(), getQ3() };<a name="line.433"></a>
<FONT color="green">434</FONT>        }<a name="line.434"></a>
<FONT color="green">435</FONT>    <a name="line.435"></a>
<FONT color="green">436</FONT>        /**<a name="line.436"></a>
<FONT color="green">437</FONT>         * Multiplies the instance by a scalar.<a name="line.437"></a>
<FONT color="green">438</FONT>         *<a name="line.438"></a>
<FONT color="green">439</FONT>         * @param alpha Scalar factor.<a name="line.439"></a>
<FONT color="green">440</FONT>         * @return a scaled quaternion.<a name="line.440"></a>
<FONT color="green">441</FONT>         */<a name="line.441"></a>
<FONT color="green">442</FONT>        public Quaternion multiply(final double alpha) {<a name="line.442"></a>
<FONT color="green">443</FONT>            return new Quaternion(alpha * q0,<a name="line.443"></a>
<FONT color="green">444</FONT>                                  alpha * q1,<a name="line.444"></a>
<FONT color="green">445</FONT>                                  alpha * q2,<a name="line.445"></a>
<FONT color="green">446</FONT>                                  alpha * q3);<a name="line.446"></a>
<FONT color="green">447</FONT>        }<a name="line.447"></a>
<FONT color="green">448</FONT>    <a name="line.448"></a>
<FONT color="green">449</FONT>        /**<a name="line.449"></a>
<FONT color="green">450</FONT>         * {@inheritDoc}<a name="line.450"></a>
<FONT color="green">451</FONT>         */<a name="line.451"></a>
<FONT color="green">452</FONT>        @Override<a name="line.452"></a>
<FONT color="green">453</FONT>        public String toString() {<a name="line.453"></a>
<FONT color="green">454</FONT>            final String sp = " ";<a name="line.454"></a>
<FONT color="green">455</FONT>            final StringBuilder s = new StringBuilder();<a name="line.455"></a>
<FONT color="green">456</FONT>            s.append("[")<a name="line.456"></a>
<FONT color="green">457</FONT>                .append(q0).append(sp)<a name="line.457"></a>
<FONT color="green">458</FONT>                .append(q1).append(sp)<a name="line.458"></a>
<FONT color="green">459</FONT>                .append(q2).append(sp)<a name="line.459"></a>
<FONT color="green">460</FONT>                .append(q3)<a name="line.460"></a>
<FONT color="green">461</FONT>                .append("]");<a name="line.461"></a>
<FONT color="green">462</FONT>    <a name="line.462"></a>
<FONT color="green">463</FONT>            return s.toString();<a name="line.463"></a>
<FONT color="green">464</FONT>        }<a name="line.464"></a>
<FONT color="green">465</FONT>    }<a name="line.465"></a>




























































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